2015/12/02 by John Morgan, Gang Tian, Morgan, John +1
Mathematics · Physics and Astronomy · #53C44 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C44
paper · pdf · doi:10.48550/arxiv.1512.00699
9 pages, 2 references
arxiv created 2015/12/02 · openalex publication_date 2015/12/02 · arxiv updated 2015/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note corrects a mistake in the original book in the evolution equations of total curvature for the curve-shrinking flow in an ambient Ricci Flow. The resulting upper bound for the evolution of total curvature is an exponential bound in time. The change involves the multiplicative constant. Here we show that it depends on the initial total curvature and the initial length, rather than just on the initial total curvature as was asserted before. This change does not affect the application of these results to prove finite-time extinction when the third homotopy group of the manifold is non-trivial.